Continuum phase transitions for bounded radial pair potentials
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Can one bounded continuous stable radial pair potential in three dimensions produce a genuine temperature phase transition in a continuum gas? The target asks for a common inverse critical temperature over an open density interval, with finite canonical free energy and sufficiently fast tail decay.
Why it matters and what counts as progress
Why it matters: One potential with a common temperature singularity over an open density interval is a stronger continuum phase-transition construction than single-density coexistence.
What counts as progress: Construct such a potential and prove a strict inverse-temperature derivative jump; extending coexistence from one density to an open interval is a further advance.
How the problem developed
- 1971 · Partial result [1]
David Ruelle Proved a phase transition for the two-species Widom–Rowlinson continuum model, a distinct interaction setting.
- 1998 · Partial result [1]
Joel Lebowitz, Eliott Mazel and Errico Presutti Proved liquid–vapor coexistence using attractive pair interactions together with repulsive four-body terms.
- 24 Sept 2026 · Reported claim [1]
OpenAI The manuscript constructs a bounded radial pair potential with algebraic decay and reports a continuum phase transition for its thermodynamic model.
AI contribution
A radial continuum phase transition with algebraic decay
One bounded continuous stable radial pair potential in three dimensions has |φ(r)|≤C r^(−3−1/32) for r≥1 and finite canonical free energy. At one common βc in [7/8,9/8], the free energy has a strict inverse-temperature derivative jump for every density in an open interval around 5p/3.
Sources
Website timeline
Publication dates and editorial changes.
OpenAI reports a continuum phase transition across a density interval